Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.0% → 99.5%

Time: 7.6s

Alternatives: 10

Speedup: 0.8×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x - x \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 (- INFINITY))
     (* z (* x y))
     (if (<= t_0 5e+87) (- x (* x t_0)) (* z (- (* x y) x))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x - (x * t_0);
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x - (x * t_0);
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (x * y)
	elif t_0 <= 5e+87:
		tmp = x - (x * t_0)
	else:
		tmp = z * ((x * y) - x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(z * Float64(x * y));
	elseif (t_0 <= 5e+87)
		tmp = Float64(x - Float64(x * t_0));
	else
		tmp = Float64(z * Float64(Float64(x * y) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = z * (x * y);
	elseif (t_0 <= 5e+87)
		tmp = x - (x * t_0);
	else
		tmp = z * ((x * y) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+87], N[(x - N[(x * t$95$0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 44.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   4. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 4.9999999999999998e87

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]

   if 4.9999999999999998e87 < (*.f64 (-.f64 1 y) z)

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 88.5%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(x \cdot z\right) \cdot \left(y - 1\right)} \]

      2. flip-- 84.1%

         \[\leadsto x + \left(x \cdot z\right) \cdot \color{blue}{\frac{y \cdot y - 1 \cdot 1}{y + 1}} \]

      3. +-commutative 84.1%

         \[\leadsto x + \left(x \cdot z\right) \cdot \frac{y \cdot y - 1 \cdot 1}{\color{blue}{1 + y}} \]

      4. associate-*r/ 81.4%

         \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \left(y \cdot y - 1 \cdot 1\right)}{1 + y}} \]

      5. metadata-eval 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \left(y \cdot y - \color{blue}{1}\right)}{1 + y} \]

      6. fma-neg 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(y, y, -1\right)}}{1 + y} \]

      7. metadata-eval 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, \color{blue}{-1}\right)}{1 + y} \]

      8. +-commutative 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{\color{blue}{y + 1}} \]

   4. Applied egg-rr 81.4%

      \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{y + 1}} \]

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{\left(x + x \cdot \left(y \cdot z\right)\right) - x \cdot z} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x - x \cdot \left(\left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 (- INFINITY))
     (* z (* x y))
     (if (<= t_0 5e+87) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (- (* x y) x))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (x * y)
	elif t_0 <= 5e+87:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * ((x * y) - x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(z * Float64(x * y));
	elseif (t_0 <= 5e+87)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(Float64(x * y) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = z * (x * y);
	elseif (t_0 <= 5e+87)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * ((x * y) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+87], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 44.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   4. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 4.9999999999999998e87

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 4.9999999999999998e87 < (*.f64 (-.f64 1 y) z)

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 88.5%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(x \cdot z\right) \cdot \left(y - 1\right)} \]

      2. flip-- 84.1%

         \[\leadsto x + \left(x \cdot z\right) \cdot \color{blue}{\frac{y \cdot y - 1 \cdot 1}{y + 1}} \]

      3. +-commutative 84.1%

         \[\leadsto x + \left(x \cdot z\right) \cdot \frac{y \cdot y - 1 \cdot 1}{\color{blue}{1 + y}} \]

      4. associate-*r/ 81.4%

         \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \left(y \cdot y - 1 \cdot 1\right)}{1 + y}} \]

      5. metadata-eval 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \left(y \cdot y - \color{blue}{1}\right)}{1 + y} \]

      6. fma-neg 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(y, y, -1\right)}}{1 + y} \]

      7. metadata-eval 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, \color{blue}{-1}\right)}{1 + y} \]

      8. +-commutative 81.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{\color{blue}{y + 1}} \]

   4. Applied egg-rr 81.4%

      \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{y + 1}} \]

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{\left(x + x \cdot \left(y \cdot z\right)\right) - x \cdot z} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -9800:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= z -9800.0)
     t_0
     (if (<= z -1.6e-88)
       t_1
       (if (<= z 4e-72) x (if (<= z 4.5e+49) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -9800.0) {
		tmp = t_0;
	} else if (z <= -1.6e-88) {
		tmp = t_1;
	} else if (z <= 4e-72) {
		tmp = x;
	} else if (z <= 4.5e+49) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = x * (y * z)
    if (z <= (-9800.0d0)) then
        tmp = t_0
    else if (z <= (-1.6d-88)) then
        tmp = t_1
    else if (z <= 4d-72) then
        tmp = x
    else if (z <= 4.5d+49) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -9800.0) {
		tmp = t_0;
	} else if (z <= -1.6e-88) {
		tmp = t_1;
	} else if (z <= 4e-72) {
		tmp = x;
	} else if (z <= 4.5e+49) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if z <= -9800.0:
		tmp = t_0
	elif z <= -1.6e-88:
		tmp = t_1
	elif z <= 4e-72:
		tmp = x
	elif z <= 4.5e+49:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -9800.0)
		tmp = t_0;
	elseif (z <= -1.6e-88)
		tmp = t_1;
	elseif (z <= 4e-72)
		tmp = x;
	elseif (z <= 4.5e+49)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -9800.0)
		tmp = t_0;
	elseif (z <= -1.6e-88)
		tmp = t_1;
	elseif (z <= 4e-72)
		tmp = x;
	elseif (z <= 4.5e+49)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9800.0], t$95$0, If[LessEqual[z, -1.6e-88], t$95$1, If[LessEqual[z, 4e-72], x, If[LessEqual[z, 4.5e+49], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9800 or 4.49999999999999982e49 < z

   1. Initial program 86.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 85.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y - 1\right)\right)} \]

   3. Taylor expanded in y around 0 60.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 60.5%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 60.5%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   5. Simplified 60.5%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -9800 < z < -1.60000000000000006e-88 or 3.9999999999999999e-72 < z < 4.49999999999999982e49

   1. Initial program 97.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 62.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   4. Simplified 62.2%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if -1.60000000000000006e-88 < z < 3.9999999999999999e-72

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9800:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17000:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{1}{y + -1}}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -17000.0)
   (* x (+ 1.0 (* z (+ y -1.0))))
   (+ x (/ z (/ (/ 1.0 (+ y -1.0)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000.0) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = x + (z / ((1.0 / (y + -1.0)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-17000.0d0)) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = x + (z / ((1.0d0 / (y + (-1.0d0))) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000.0) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = x + (z / ((1.0 / (y + -1.0)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17000.0:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = x + (z / ((1.0 / (y + -1.0)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17000.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(1.0 / Float64(y + -1.0)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -17000.0)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = x + (z / ((1.0 / (y + -1.0)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17000.0], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(1.0 / N[(y + -1.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -17000

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if -17000 < x

   1. Initial program 90.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 90.8%

         \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]

      2. flip-- 82.0%

         \[\leadsto x \cdot \left(1 - z \cdot \color{blue}{\frac{1 \cdot 1 - y \cdot y}{1 + y}}\right) \]

      3. associate-*r/ 79.0%

         \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z \cdot \left(1 \cdot 1 - y \cdot y\right)}{1 + y}}\right) \]

      4. metadata-eval 79.0%

         \[\leadsto x \cdot \left(1 - \frac{z \cdot \left(\color{blue}{1} - y \cdot y\right)}{1 + y}\right) \]

      5. pow2 79.0%

         \[\leadsto x \cdot \left(1 - \frac{z \cdot \left(1 - \color{blue}{{y}^{2}}\right)}{1 + y}\right) \]

   3. Applied egg-rr 79.0%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z \cdot \left(1 - {y}^{2}\right)}{1 + y}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 82.0%

         \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z}{\frac{1 + y}{1 - {y}^{2}}}}\right) \]

   5. Simplified 82.0%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z}{\frac{1 + y}{1 - {y}^{2}}}}\right) \]
   6. Step-by-step derivation

      1. sub-neg 82.0%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\frac{z}{\frac{1 + y}{1 - {y}^{2}}}\right)\right)} \]

      2. +-commutative 82.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\frac{z}{\frac{1 + y}{1 - {y}^{2}}}\right) + 1\right)} \]

   7. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y + -1\right) \cdot x\right) + x} \]
   8. Step-by-step derivation

      1. *-commutative 97.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1\right)\right)} + x \]

      2. associate-*r* 98.4%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot \left(y + -1\right)} + x \]

      3. *-commutative 98.4%

         \[\leadsto \color{blue}{\left(x \cdot z\right)} \cdot \left(y + -1\right) + x \]

      4. metadata-eval 98.4%

         \[\leadsto \left(x \cdot z\right) \cdot \left(y + \color{blue}{\left(-1\right)}\right) + x \]

      5. sub-neg 98.4%

         \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{\left(y - 1\right)} + x \]

      6. flip-- 85.8%

         \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{\frac{y \cdot y - 1 \cdot 1}{y + 1}} + x \]

      7. metadata-eval 85.8%

         \[\leadsto \left(x \cdot z\right) \cdot \frac{y \cdot y - \color{blue}{1}}{y + 1} + x \]

      8. fma-neg 85.8%

         \[\leadsto \left(x \cdot z\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(y, y, -1\right)}}{y + 1} + x \]

      9. metadata-eval 85.8%

         \[\leadsto \left(x \cdot z\right) \cdot \frac{\mathsf{fma}\left(y, y, \color{blue}{-1}\right)}{y + 1} + x \]

      10. clear-num 85.8%

          \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{\frac{1}{\frac{y + 1}{\mathsf{fma}\left(y, y, -1\right)}}} + x \]

      11. div-inv 85.8%

          \[\leadsto \color{blue}{\frac{x \cdot z}{\frac{y + 1}{\mathsf{fma}\left(y, y, -1\right)}}} + x \]

      12. *-commutative 85.8%

          \[\leadsto \frac{\color{blue}{z \cdot x}}{\frac{y + 1}{\mathsf{fma}\left(y, y, -1\right)}} + x \]

      13. associate-/l* 85.3%

          \[\leadsto \color{blue}{\frac{z}{\frac{\frac{y + 1}{\mathsf{fma}\left(y, y, -1\right)}}{x}}} + x \]

      14. clear-num 85.3%

          \[\leadsto \frac{z}{\frac{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, y, -1\right)}{y + 1}}}}{x}} + x \]

      15. metadata-eval 85.3%

          \[\leadsto \frac{z}{\frac{\frac{1}{\frac{\mathsf{fma}\left(y, y, \color{blue}{-1}\right)}{y + 1}}}{x}} + x \]

      16. fma-neg 85.3%

          \[\leadsto \frac{z}{\frac{\frac{1}{\frac{\color{blue}{y \cdot y - 1}}{y + 1}}}{x}} + x \]

      17. metadata-eval 85.3%

          \[\leadsto \frac{z}{\frac{\frac{1}{\frac{y \cdot y - \color{blue}{1 \cdot 1}}{y + 1}}}{x}} + x \]

      18. flip-- 98.1%

          \[\leadsto \frac{z}{\frac{\frac{1}{\color{blue}{y - 1}}}{x}} + x \]

      19. sub-neg 98.1%

          \[\leadsto \frac{z}{\frac{\frac{1}{\color{blue}{y + \left(-1\right)}}}{x}} + x \]

      20. metadata-eval 98.1%

          \[\leadsto \frac{z}{\frac{\frac{1}{y + \color{blue}{-1}}}{x}} + x \]

   9. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{z}{\frac{\frac{1}{y + -1}}{x}}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17000:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{1}{y + -1}}{x}}\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 0.019)))
   (* z (- (* x y) x))
   (+ x (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 0.019)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.1d0)) .or. (.not. (z <= 0.019d0))) then
        tmp = z * ((x * y) - x)
    else
        tmp = x + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 0.019)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1) or not (z <= 0.019):
		tmp = z * ((x * y) - x)
	else:
		tmp = x + (x * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 0.019))
		tmp = Float64(z * Float64(Float64(x * y) - x));
	else
		tmp = Float64(x + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1) || ~((z <= 0.019)))
		tmp = z * ((x * y) - x);
	else
		tmp = x + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 0.0189999999999999995 < z

   1. Initial program 86.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 86.6%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(x \cdot z\right) \cdot \left(y - 1\right)} \]

      2. flip-- 91.0%

         \[\leadsto x + \left(x \cdot z\right) \cdot \color{blue}{\frac{y \cdot y - 1 \cdot 1}{y + 1}} \]

      3. +-commutative 91.0%

         \[\leadsto x + \left(x \cdot z\right) \cdot \frac{y \cdot y - 1 \cdot 1}{\color{blue}{1 + y}} \]

      4. associate-*r/ 87.4%

         \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \left(y \cdot y - 1 \cdot 1\right)}{1 + y}} \]

      5. metadata-eval 87.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \left(y \cdot y - \color{blue}{1}\right)}{1 + y} \]

      6. fma-neg 87.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(y, y, -1\right)}}{1 + y} \]

      7. metadata-eval 87.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, \color{blue}{-1}\right)}{1 + y} \]

      8. +-commutative 87.4%

         \[\leadsto x + \frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{\color{blue}{y + 1}} \]

   4. Applied egg-rr 87.4%

      \[\leadsto x + \color{blue}{\frac{\left(x \cdot z\right) \cdot \mathsf{fma}\left(y, y, -1\right)}{y + 1}} \]

   5. Taylor expanded in y around inf 78.8%

      \[\leadsto \color{blue}{\left(x + x \cdot \left(y \cdot z\right)\right) - x \cdot z} \]

   6. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - x\right)} \]

   if -1.1000000000000001 < z < 0.0189999999999999995

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]

   3. Taylor expanded in y around inf 98.7%

      \[\leadsto x + \color{blue}{x \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.7%

         \[\leadsto x + x \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 98.7%

      \[\leadsto x + \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e+34)
   (* x (+ 1.0 (* z (+ y -1.0))))
   (+ x (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+34) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = x + (z * (x * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2d+34)) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = x + (z * (x * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+34) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = x + (z * (x * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e+34:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = x + (z * (x * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e+34)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + Float64(z * Float64(x * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e+34)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = x + (z * (x * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e+34], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999989e34

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if -1.99999999999999989e34 < x

   1. Initial program 91.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]

      2. flip-- 82.2%

         \[\leadsto x \cdot \left(1 - z \cdot \color{blue}{\frac{1 \cdot 1 - y \cdot y}{1 + y}}\right) \]

      3. associate-*r/ 79.2%

         \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z \cdot \left(1 \cdot 1 - y \cdot y\right)}{1 + y}}\right) \]

      4. metadata-eval 79.2%

         \[\leadsto x \cdot \left(1 - \frac{z \cdot \left(\color{blue}{1} - y \cdot y\right)}{1 + y}\right) \]

      5. pow2 79.2%

         \[\leadsto x \cdot \left(1 - \frac{z \cdot \left(1 - \color{blue}{{y}^{2}}\right)}{1 + y}\right) \]

   3. Applied egg-rr 79.2%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z \cdot \left(1 - {y}^{2}\right)}{1 + y}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 82.2%

         \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z}{\frac{1 + y}{1 - {y}^{2}}}}\right) \]

   5. Simplified 82.2%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{z}{\frac{1 + y}{1 - {y}^{2}}}}\right) \]
   6. Step-by-step derivation

      1. sub-neg 82.2%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\frac{z}{\frac{1 + y}{1 - {y}^{2}}}\right)\right)} \]

      2. +-commutative 82.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\frac{z}{\frac{1 + y}{1 - {y}^{2}}}\right) + 1\right)} \]

   7. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y + -1\right) \cdot x\right) + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+37} \lor \neg \left(y \leq 1.05 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+37) (not (<= y 1.05e+19))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+37) || !(y <= 1.05e+19)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.4d+37)) .or. (.not. (y <= 1.05d+19))) then
        tmp = x * (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+37) || !(y <= 1.05e+19)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+37) or not (y <= 1.05e+19):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+37) || !(y <= 1.05e+19))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+37) || ~((y <= 1.05e+19)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+37], N[Not[LessEqual[y, 1.05e+19]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e37 or 1.05e19 < y

   1. Initial program 86.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 67.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   4. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if -2.4e37 < y < 1.05e19

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+37} \lor \neg \left(y \leq 1.05 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+22} \lor \neg \left(y \leq 2120000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+22) (not (<= y 2120000000000.0)))
   (* z (* x y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+22) || !(y <= 2120000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.9d+22)) .or. (.not. (y <= 2120000000000.0d0))) then
        tmp = z * (x * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+22) || !(y <= 2120000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e+22) or not (y <= 2120000000000.0):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e+22) || !(y <= 2120000000000.0))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e+22) || ~((y <= 2120000000000.0)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e+22], N[Not[LessEqual[y, 2120000000000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000002e22 or 2.12e12 < y

   1. Initial program 85.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 76.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 76.7%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   4. Simplified 76.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if -1.9000000000000002e22 < y < 2.12e12

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+22} \lor \neg \left(y \leq 2120000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 64.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.019))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.019)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.019d0))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.019)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.019):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.019))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.019)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.0189999999999999995 < z

   1. Initial program 86.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 85.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y - 1\right)\right)} \]

   3. Taylor expanded in y around 0 58.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.2%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 58.2%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 58.2%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   5. Simplified 58.2%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -1 < z < 0.0189999999999999995

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 68.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 93.3%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 35.9%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 35.9%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023336 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))